During one of my perpetual forages into Google looking for arcane information
on Morphy, I came across
this site about
a Esplanade Avenue
walking tour which offered up this information:

Denis-Morphy-Barnett Houses, nos. 600-06, were all constructed in 1834 by
attorney Henry Raphael Denis on what was once three separate lots. The
common-wall townhouses were basically all designed in the same style, although
they appear as three distinct houses today, thanks to alterations through the
years. The house at no. 600 has the particular distinction of having been owned
by Alonzo Morphy, the father of famed chess master Paul Morphy.
The gorgeous lacy two-level wraparound cast-iron balconies were added in the
1850s. The house at 604 originally possessed an entresol, or half-story, with
Gothic arches, and the house at 606 was remodeled in 1859 in the Greek Revival
style. It was once owned by Michel Bringier of l'Hermitage Plantation upriver
from New Orleans.

Intriguing! I never realized that Judge Morphy owned a house on
Esplanade Avenue.

However, I had to
corroborate this information, so I continued my search... and soon found myself
on a site I've used many times
in the past which did, indeed confirm this information saying that:

In 1809 Charles
Louis Blache, Dame Felicite and Modeste Blache (Morphy's maternal grandmother)
received properties at 1205 Royal Street, 1211 Royal Street and 1215 Royal
Street from Jean Joseph Blache. In 1818 the property was sold to Martin
Bourgeat (who, in turn, sold it to Jean Mercier and Dominque Bouligny in 1830)

In 1841 Joseph Le
Carpentier bought the properties at 1235-1241 Royal Steet from Auguste O'Duhigg.
In 1885 the propery housed a furniture store (from newspaper reports on a fire
at that location).